Abstract
This work deals with the analysis of the mechanical bending behavior of a rectangular plate simply supported on four sides (FGM), subjected to transverse static loading. The high order theory is used in this work, The developed models are variably consistent, have a strong similarity with the classical plate theory in many aspects, do not require correction to the shear factor, and give rise to variations transverse shear stresses such as transverse shear parabolically varies across the shear thickness and satisfies surface conditions without stresses. Equilibrium equations are obtained by applying the principle of virtual works. The mathematical expressions of the arrow, the stresses are obtained using Navies approach to solve the system of equilibrium equations. The influence of mechanical loading and the change of the parameter of the material on mechanical behavior of the plate P-FGM are represented by a numerical example.
Highlights
In recent years, functionally graded materials (FGM) have attracted considerable attention in many applications in engineering
Understanding the mechanical behavior of an FGM plate is very important in estimating the safety of the plate (Reddy,. 1984). (Woo & Meguid, 2001) have applied the Karman theory for the large deformation to obtain the analytical solution for the plates and shells under a mechanical loading transverse and a field of temperature. (Praveen & Reddy, 1998) studied the static and dynamic responses of thick
This work consists of demonstrating the theoretical plate solutions of FGM functional gradient materials under transverse loading developed using high order theory or refined theory (RPT)
Summary
Functionally graded materials (FGM) have attracted considerable attention in many applications in engineering. (Woo & Meguid, 2001) have applied the Karman theory for the large deformation to obtain the analytical solution for the plates and shells under a mechanical loading transverse and a field of temperature. This study deals with the analysis of the mechanical behavior at the static flexion of a rectangular plate of FGM functional gradient materials with the theory of refined shear deformation plates. An efficient and simple refined plate theory (RPT) was initially introduced and implemented by (Shimpi & Patel, 2006) in order to deal with the problems of static and dynamic analysis of orthotropic plates. The transverse displacement (w) of the RPT is composed of two components of the displacement due to bending (wb) and shear (ws).To apply the improved theory for analyzing plate problems (Merdaci et al,. 2011), it is begun with the Constitutive equations that take the form as,
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